根据电动力学理论、板壳磁弹性理论和结构随机振动理论,导出电磁场中矩形薄板的磁弹性非线性随机振动方程,然后利用伽辽金法对四边简支矩形薄板的非线性随机振动方程进行整理,得到伊藤型状态方程;在外界激励是平稳高斯白噪声的条件下,利用稳态的FPK方程法求解得到薄板的稳态随机振动位移和速度响应的多个数字特征;通过具体数值算例分析,讨论了电磁参数对各数字特征的影响。
Abstract
According to the theory of electrodynamics, the magneto-elastic theory of plates and shells, and the theory of structure’s random vibration, the magneto-elastic nonlinear random vibration equation of a plate simply supported in an electromagnetic field is derived. And then, the nonlinear random vibration equation is changed into the ITO equation using the Galerkin method. The numerical characteristics of the displacement and speed responses of the stationary random vibration are gotten by using FPK equations method when the external excitation is stationary Gauss white noise. The influences of the parameters of the electromagnetic field to the numerical characteristics are discussed in the numerical example.
Key words
magneto-elasticity /
nonlinearity /
random vibration /
rectangular thin plate
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] L. V. Mol'chenko, I. I. Loos. Magneto-elastic nonlinear deformation of a conical shell of variable stiffness[J]. International Applied Mechanics, 1999, 35(11): 34-39
[2] L. V. Mol'chenko. Nonlinear deformation of current-carrying plates in a non-steady magnetic field[J]. Soviet Applied Mechanics (English Translation of Prikladnaya Mekhanika), 1990, 26(6): 555-558
[3] 周又和,郑晓静著. 电磁固体结构力学[M]. 北京:科学出版社, 1999
[4] 胡宇达. 传导薄板的非线性磁弹性振动问题[J]. 工程力学, 2001, 18(4): 89-94
HU YuDa.Magneto-elastic nonlinear vibration of a thin conductive plate[J]. Engineering Mechanics, 2001, 18(4): 89-94(In Chinese).
[5] 王平, 李晓靓, 白象忠, 王知人. 导电梁在磁场中的磁弹性随机振动[J]. 振动与冲击, 2007,
26(3): 75-78
WANG Ping,LI Xiao-jing,BAI Xiang-zhong.Magneto-elastic random vibration of
an electro-conductive beam in magnetic field[J].Journal of Vibration and Shock.
2007, 26(3): 75-78.
[6] 王平, 李晓靓, 刘强. 导电薄板在磁场中的磁弹性随机振动[J]. 振动与冲击, 2009, 28(1):
138-142.
WANG Ping,LI Xiao-jing,LIU Qiang. Magneto-elastic random vibration of an electro-
conductive plate in magnetic field[J].Journal of Vibration and Shock.2009,28(1):
138-142.
[7] G. Yang, B. Sh. Zhao. The refined theory for a magnetoelastic body-I plate problems[J].
International Journal of Applied Electromagnetics and Mechanics, 2009, 29: 1-14
[8] D. J. Hasanyan, Davresh, Librescu, Liviu. Nonlinear vibration of finitely electro-conductive
plate-strips in a magnetic field[J]. Computers and Structures, 2005, 83: 1205-1216
[9] B. Moon, C. T. Lee, B. S. Kang, B. S. Kim. Statistical Random Response Analysis and Reliability
Design of Structure System with Non-linearity[J]. Mechanical Systems and Signal Processing,
2005,19:1135-1151
[10] T. P. Chang, H. C. Chang, M. F. Liu. A Finite Element Analysis on Random Vibration of Nonlinear
Shell Structures[J]. Journal of Sound and Vibration, 2006, (291): 240-257
[11] 白象忠, 田振国. 板壳磁弹性力学基础[M]. 北京: 科学出版社, 2006
BAI XiangZhong, TIAN ZhengGuo. Foundamental magneto-elasticity theory of plate and shells[M].
Beijing:Sciences Press, 2006: 181-182(In Chinese).
[12] 陈予恕,唐云等.非线性动力学中的现代分析方法[M]. 北京:科学出版社, 2000,221-223.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}